Table 1. Baseline Characteristics
Characteristic Overall
N = 1801		 ABC
N = 301		 ACB
N = 301		 BAC
N = 301		 BCA
N = 301		 CAB
N = 301		 CBA
N = 301		 p-value2
Age (years) 32 (8) [18, 45] 33 (8) [19, 44] 31 (7) [18, 42] 31 (7) [20, 44] 33 (8) [19, 45] 32 (7) [21, 44] 31 (7) [20, 44] 0.6
Race






0.9
    Black 64 (36%) 12 (40%) 13 (43%) 12 (40%) 10 (33%) 8 (27%) 9 (30%)
    White 52 (29%) 8 (27%) 9 (30%) 7 (23%) 7 (23%) 12 (40%) 9 (30%)
    Other 64 (36%) 10 (33%) 8 (27%) 11 (37%) 13 (43%) 10 (33%) 12 (40%)
Female 81 (45%) 13 (43%) 11 (37%) 16 (53%) 14 (47%) 12 (40%) 15 (50%) 0.8
1 Mean (SD) [Min, Max]; n (%)
2 Kruskal-Wallis rank sum test; Pearson’s Chi-squared test

preliminary assessment and comparison of systemic and local Pharmacokinetics (PK) of Pill A, Gel B, and Gel C

No apparent difference in starting value by period or treatment, so looking at change from baseline in PK

Notation: \(k =\) subject, \(i =\) sequence, \(j =\) period,

\[ \begin{align} k:& \text{subject}, k = 1,...,180\\ j:& \text{sequence}, j=0,1,2\\ i:& \text{period}, i=1,2,3\\ \pi:& \text{period effect}\\ \tau:& \text{treatment effect}\\ \lambda:& \text{sequence/carryover effect}\\ b:& \text{subject-specific intercepts}\\ \varepsilon:& \text{residual error}\\ \end{align} \]

{ijk}:& \ {ijk}:& \

Blood PK Change by Treatment

\[ Y_{ik} = \mu + b_{ik} + \pi_i + \tau_{i} + \lambda_i+\varepsilon_{ik}, \quad b_{ik} \sim N(0, \sigma_b^2), \quad \varepsilon_{ik} \sim N(0, \sigma^2) \]

Findings: Significantly less decrease in gels vs pill A

Comparison Beta 95% CI p-value
Intercept (Pill A, Period 1, Sequence 0) 120.7 115.5, 125.9 <0.001
Treatment

<0.001
    Gel B vs Pill A -10.9 -15.5, -6.3
    Gel C vs Pill A -11.7 -16.2, -7.1
Period

0.7
    Period 2 vs Period 1 -1.5 -6.1, 3.1
    Period 3 vs Period 1 -1.7 -6.3, 2.9
Sequence

0.6
    Sequence 1 vs Sequence 0 2.3 -2.9, 7.4
    Sequence 2 vs Sequence 0 2.4 -2.7, 7.6
Abbreviation: CI = Confidence Interval

Skin PK Change by Treatment

\[ Y_{i} = \mu + \pi_i + \tau_{i} + \lambda_{i} + \varepsilon_{i}, \quad \varepsilon_{i} \sim N(0, \sigma^2) \]

Findings: Significantly less decrease in gels vs pill A

Comparison Beta 95% CI p-value
Intercept (Pill A, Period 1, Sequence 0) 205.9 197.7, 214.1 <0.001
Treatment

<0.001
    Gel B vs Pill A -32.4 -40.0, -24.8
    Gel C vs Pill A -41.9 -49.5, -34.3
Period

0.8
    Period 2 vs Period 1 2.5 -5.1, 10.1
    Period 3 vs Period 1 1.3 -6.3, 8.9
Sequence

0.7
    Sequence 1 vs Sequence 0 -2.9 -10.5, 4.6
    Sequence 2 vs Sequence 0 -1.9 -9.5, 5.7
Abbreviation: CI = Confidence Interval

assess the correlation of PK with adherence measures and the occurrence of adverse events

Skin PK

\[ Y_{i} = \mu + \pi_i + \tau_{i} + \lambda_{i} + \alpha_{i} + \beta_{i} +\varepsilon_{i}, \quad \varepsilon_{i} \sim N(0, \sigma^2) \]

Skin/Blood PK ~ Random Intercept (Subject) + Treatment + Adherence + Carryover + Period

## 
## Call:
## lm(formula = skinVL_change ~ treatment + overall_adhere + overall_safety + 
##     sequence_ind + period, data = merged)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -109.465  -21.844    0.291   21.087  115.767 
## 
## Coefficients:
##                                Estimate Std. Error t value             Pr(>|t|)
## (Intercept)                    107.5583    10.0754  10.675 < 0.0000000000000002
## treatmentGel B                 -24.3354     3.6291  -6.706      0.0000000000514
## treatmentGel C                 -36.9474     3.5469 -10.417 < 0.0000000000000002
## overall_adhere                   1.8330     0.2753   6.658      0.0000000000696
## overall_safetyNo Adverse Event  56.3456     5.2241  10.786 < 0.0000000000000002
## sequence_ind1                   -5.7254     3.4564  -1.656               0.0982
## sequence_ind2                   -3.0500     3.4499  -0.884               0.3770
## periodperiod2                    0.8405     3.4511   0.244               0.8077
## periodperiod3                    1.6260     3.4483   0.472               0.6375
##                                   
## (Intercept)                    ***
## treatmentGel B                 ***
## treatmentGel C                 ***
## overall_adhere                 ***
## overall_safetyNo Adverse Event ***
## sequence_ind1                  .  
## sequence_ind2                     
## periodperiod2                     
## periodperiod3                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.71 on 531 degrees of freedom
## Multiple R-squared:  0.3614, Adjusted R-squared:  0.3517 
## F-statistic: 37.56 on 8 and 531 DF,  p-value: < 0.00000000000000022
Comparison Beta 95% CI p-value
Intercept (Pill A, Period 1, Sequence 0, No Adherence or AE) 107.6 87.8, 127.4 <0.001
Treatment

<0.001
    Gel B vs Pill A -24.3 -31.5, -17.2
    Gel C vs Pill A -36.9 -43.9, -30.0
Additional Day of Adherence 1.8 1.3, 2.4 <0.001
Adverse Event

<0.001
    Adverse Event — —
    No Adverse Event 56.3 46.1, 66.6
Sequence

0.3
    1 vs 0 -5.7 -12.5, 1.1
    2 vs 0 -3.1 -9.8, 3.7
Period

0.9
    Period 2 vs Period 1 0.8 -5.9, 7.6
    Period 3 vs Period 1 1.6 -5.1, 8.4
Abbreviation: CI = Confidence Interval

Blood PK

\[ Y_{ik} = \mu + b_{ik} + \pi_i + \tau_{i} + \lambda_{i} + \alpha_{ik} + \beta_{ik} + \varepsilon_{ik}, \quad b_{ik} \sim N(0, \sigma_b^2), \quad \varepsilon_{ik} \sim N(0, \sigma^2) \]

Comparison Beta 95% CI p-value
Intercept (Pill A, Period 1, Sequence 0, No Adherence or AE) 72.7 59.3, 86.1 <0.001
Treatment

<0.001
    Gel B vs Pill A -6.8 -11.4, -2.2
    Gel C vs Pill A -9.1 -13.6, -4.6
Additional Day of Adherence 0.9 0.6, 1.3 <0.001
Adverse Event

<0.001
    Adverse Event — —
    No Adverse Event 26.4 19.6, 33.2
Sequence

0.7
    1 vs 0 0.9 -3.8, 5.7
    2 vs 0 1.9 -2.9, 6.6
Period

0.6
    Period 2 vs Period 1 -2.3 -6.7, 2.1
    Period 3 vs Period 1 -1.5 -5.9, 2.8
Abbreviation: CI = Confidence Interval